1. Выполните действие: a) \(\frac{5}{7}:\frac{5}{11}\); б) \(\frac{6}{25}:\frac{5}{18}\); в) 3\(\frac{1}{5}\cdot\frac{1}{9}\); г) 1\(\frac{3}{7}\cdot14\); д) \(\frac{5}{9}:\frac{10}{27}\); е) \(\frac{12}{13}:6\).

Решение:

1. \(\frac{5}{7}:\frac{5}{11}=\frac{5}{7}\cdot\frac{11}{5}=\frac{5\cdot11}{7\cdot5}=\frac{11}{7}=1\frac{4}{7}\)
2. \(\frac{6}{25}:\frac{5}{18}=\frac{6}{25}\cdot\frac{18}{5}=\frac{6\cdot18}{25\cdot5}=\frac{108}{125}\)
3. 3\(\frac{1}{5}\cdot\frac{1}{9}=\frac{16}{5}\cdot\frac{1}{9}=\frac{16\cdot1}{5\cdot9}=\frac{16}{45}\)
4. 1\(\frac{3}{7}\cdot14=\frac{10}{7}\cdot14=\frac{10\cdot14}{7}=\frac{10\cdot2}{1}=20\)
5. \(\frac{5}{9}:\frac{10}{27}=\frac{5}{9}\cdot\frac{27}{10}=\frac{5\cdot27}{9\cdot10}=\frac{1\cdot3}{1\cdot2}=\frac{3}{2}=1\frac{1}{2}\)
6. \(\frac{12}{13}:6=\frac{12}{13}:\frac{6}{1}=\frac{12}{13}\cdot\frac{1}{6}=\frac{12\cdot1}{13\cdot6}=\frac{2\cdot1}{13\cdot1}=\frac{2}{13}\)

Ответ:

1. \(1\frac{4}{7}\)
2. \(\frac{108}{125}\)
3. \(\frac{16}{45}\)
4. 20
5. \(1\frac{1}{2}\)
6. \(\frac{2}{13}\)